They can change their helmets, jerseys, and logo, but not the lack of logic that has defined them since 1969.

You can change their colors, but not their character.

You can move from Shea Stadium, hop the Hudson River, and start anew in New Jersey. Yet not even the industrial waste and smell of the swamp can erase the stench from a franchise that just never gets it right.

The New York Jets are an enigma. At their best, a confounding, confusing franchise that has played some form of football schizophrenia for 45 years. The Jets last won a Super Bowl the year yours truly was born. And, at this rate, the Jets will leave their fans unfulfilled for another 45 years.

Just when they get you geeked up, dart out to 4-1 record, with a new general manager, new head coach, new heading, Gang Green turns gangrenous, swallowed up by the black hole of ineptitude that has so sadly become their hallmark, their .500 record doubling as their logo.

The Jets and Houston Texans are 5-5, yet could two teams with the same record look and feel any different? And as they passed each other Sunday, the Texans tormented the Jets en route to 24-17 win. Like most games the Jets lose, like most seasons the Jets squander, they could have easily won this game, yet it feels like they lost by four touchdowns.

After a plodding preseason, the Jets entered the regular season with few expectations. Then they churned out four wins in five games, making Todd Bowles look like a magician, Ryan Fitzpatrick look like an overnight, Mennonite sensation, and their defense turning into the most ornery in the sport.

Darrelle Revis came home. As did Bowles, the local kid from Elizabeth, New Jersey, just 20 minutes away, making good for his hometown team. Two feel-great stories in a season bursting with possibilities.

Then the dream cloud popped and the nightmare began, as it always does for the Jets.

T.J. Yates, Houston’s third starting QB this season, and making his first start in nearly four years, looked like he, not Fitzpatrick, had been at the helm from the jump of 2015. The Jets had problems running and passing, stopping the run and pass, and passed up another chance to keep their nostrils above the .500 waters, their playoff prospects are now in serious jeopardy. And now the Texans, who were imploding in September, have the same record as the Jets in November.

Beyond the obvious, ominous signs of a team that has gone 1-4 since starting 4-1, the Jets can’t rely on their bedrock ballers to climb out of the sudden chasm they’ve created. Chris Ivory looks nothing like the wild bull who’d bowled over opponents in September and October.

Revis, who signed an epic contract to return home, where he turned Manhattan into Revis Island, looks like he’s lost a step, or two, or three, or however many times DeAndre Hopkins torched the future Hall of Famer.

No matter how cozy the narrative feels, the idea that you can come home again, the truth is that Revis is 30, at a position that doesn’t suffer his age and wage very kindly. While he may be in his prime in the game of life, the game of football seems to be speeding past his prime.

Hopkins didn’t just beat Revis on that sublime sideline catch, where he snagged that ball with his left hand, tucked it into his tummy, and tapped two balletic feet just inside the sideline. Hopkins juked his way free on another play, then sped down the middle, toward the goal line, while a long pass nestled nicely into his chest, as Revis chased, panted, then lunged short of Hopkins, who sauntered into the end zone. Revis lay face-first on the turf, looking up helplessly at Hopkins. It was a perfect microcosm of the season.

Ivory rolled his way to 460 yards through four games. If you take away his Nov. 12 performance, he’s had just 118 yards in four subsequent games, and has totaled just 219 yards in all five games since Oct. 18.

After averaging 7.3 yards per carry against the Redskins (Oct. 18), Ivory’s next three games saw an average of 2.4, 1.1, and 1.1 yards per rush. He had four touchdowns after four games, and just two TDs over the next five. While he’s on the right side of 30 years old, the 27-year-old has a dense running style that tends to accelerate the aging process.

While Fitzpatrick plays inspired football, literally lunging into linebackers to get a first down or touchdown, the Jets’ QB is also breaking down. He’s fresh off the operating table (thumb) and has wobbled his way back to the sideline after several bone-crunching blows. You need your QB playing with his head, not leading with it, especially a Harvard Man who relies more on guile than greatness.

The Jets, who looked fresh and fun and ready to shock the Big Apple with a big season, suddenly look old and worn and weak. Their biggest defensive play was preventing J.J. Watt from catching his fourth career TD in as many tries.

Otherwise, they couldn’t stop Yates, who was in his first start since January 2012. They couldn’t stop Hopkins, whom everyone knew was Yates’s top target all game. They couldn’t contain Alfred Blue, a backup running back who doesn’t have a fraction of Arian Foster’s talent. They even let a wide receiver toss a TD pass.

There is no doubt Jets Nation will look for silver linings in a season suddenly slipping away. As the Jets plunge from the rungs of relevance, it’s time for a gut-check during a gut-wrenching schedule that still showcases their local war with the Giants, the Romo-led Cowboys, Rex Ryan’s Bills, and, yes, the New England Patriots, who will not ease off the throttle even if they have already bagged the AFC East, or even the AFC.

Name the Jets tight end. Exactly. Quincy Enunwa and Wesley Johnson are among the epic skill players who got the rock at some point yesterday. Johnson, of course, is an offensive lineman. Jace Amaro was supposed to fill the role for the Jets, but tore his labrum in August. Jeff Cumberland had five catches — all season. Kellen Davis has one.

Tight end isn’t the main reason the Jets are twirling down the NFL toilet. But it’s emblematic of the larger problem. The Jets have no identity anymore. They were a run-first offense, stopped the run on defense, and then unleashed the “Sons of Anarchy” rabid pass rush.

Now they no longer haunt the opposing QB, nor do they protect their own. The Texans mauled the Jets’ offensive line, had no issues throwing the ball, their career backup (Yates) slicing up the Jets’ enervated — and now impotent — secondary.

Of course, the Jets could return, win a couple games, and get back in the mix. But do you have any trust that they will? The NFL flaunts itself as a league of parity, though the Jets are looking more and more like a parody.

You saw two .500 teams on the field Sunday, yet they could not be moving in more different directions. The Texans came out of “Hard Knocks” looking like world-beaters, then tripped out of the gate, looking like an expansion franchise. At 1-4, there was little hope for Houston.

Conversely, the Jets were 4-1, and looking like world-beaters. And know look like they were hard-knocked into irrelevance. Going from Gang Green to gangrene in a matter of bad, NFL moments.